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On the new wave solutions to a nonlinear model arising in plasma physics

  • Onur Alp IlhanEmail author
  • Tukur Abdulkadir Sulaiman
  • Hasan Bulut
  • Haci Mehmet Baskonus
Regular Article

Abstract.

In this paper, we utilize the sine-Gordon expansion method and construct some travelling wave solutions to the (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation which arises in plasma physics. We successfully obtain some hyperbolic function solutions to this equation. By choosing some suitable values of parameters, we perform the numerical simulation of all the obtained solutions in this study. We observed that our result may be useful in detecting some ion-acoustic waves behaviors in a magnetized plasma. All the computations and graphic plots in this article are performed with the aid of the Mathematica package.

References

  1. 1.
    H. Jafari, R. Soltani, C.M. Khalique, D. Baleanu, Bound. Value Probl. 2013, 117 (2013)CrossRefGoogle Scholar
  2. 2.
    M. Matinfar, M. Eslami, S. Roshandel, Pramana J. Phys. 85, 593 (2015)ADSCrossRefGoogle Scholar
  3. 3.
    Z. Zhang, J. Zhong, S.S. Dou, J. Liu, D. Peng, T. Gao, Rom. Rep. Phys. 65, 1155 (2013)Google Scholar
  4. 4.
    N. Taghizadeh, M. Mirzazadeh, A.S. Paghaleh, Appl. Appl. Math. 7, 117 (2012)MathSciNetGoogle Scholar
  5. 5.
    M.F. El-Sabbagh, S.I. El-Ganaini, Appl. Math. Sci. 6, 3893 (2012)MathSciNetGoogle Scholar
  6. 6.
    H. Jafari, N. Kadkhoda, C.M. Khalique, Comput. Math. Appl. 64, 2084 (2012)MathSciNetCrossRefGoogle Scholar
  7. 7.
    H. Jafari, N. Kadkhoda, A. Biswas, J. King Saud Univ. Sci. 25, 57 (2013)CrossRefGoogle Scholar
  8. 8.
    M.M. Kabir, R. Bagherzadeh, Middle-East J. Sci. Res. 9, 602 (2011)Google Scholar
  9. 9.
    M. Wang, X. Li, J. Zhang, Phys. Lett. A 372, 417 (2008)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    S. Guo, Y. Zhou, X. Zhao, Appl. Math. Comput. 215, 3214 (2010)MathSciNetGoogle Scholar
  11. 11.
    H.L. Lü, X.Q. Liu, L. Niu, Appl. Math. Comput. 215, 3811 (2010)MathSciNetGoogle Scholar
  12. 12.
    N. Kadkhoda, H. Jafari, Iran. J. Numer. Anal. Optim. 6, 43 (2016)Google Scholar
  13. 13.
    M.S. Islam, K. Khan, A.H. Arnous, New Trends Math. Sci. 3, 46 (2015)MathSciNetGoogle Scholar
  14. 14.
    E.M.E. Zayed, G.M. Moatimid, A. Al-Nowehy, Sci. J. Math. Res. 5, 19 (2015)Google Scholar
  15. 15.
    A.M.A. Khater, G.M. Moatimid, A. Al-Nowehy, Global J. Sci. Front. Res. F 15, 69 (2015)Google Scholar
  16. 16.
    E.M.E. Zayed, A.H. Arnous, Sci. Res. Essays 8, 1973 (2013)Google Scholar
  17. 17.
    M. Mirzazadeh, Inf. Sci. Lett. 3, 1 (2014)CrossRefGoogle Scholar
  18. 18.
    D.J. Evans, K.R. Raslan, Int. J. Comput. Math. 82, 897 (2005)MathSciNetCrossRefGoogle Scholar
  19. 19.
    E. Fan, Phys. Lett. A 277, 212 (2000)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    R. Abazari, Rom. J. Phys. 59, 3 (2014)MathSciNetGoogle Scholar
  21. 21.
    S. Asghar, M. Mushtaq, A.H. Kara, Appl. Math. Modell. 32, 2936 (2008)CrossRefGoogle Scholar
  22. 22.
    M. Belić, N.Z. Petrović, W.P. Zhong, R.H. Xie, G. Chen, Phys. Lett. A 101, 0123904 (2008)CrossRefGoogle Scholar
  23. 23.
    S. Liu, Z. Fu, S. Liu, Q. Zhao, Phys. Lett. A 289, 69 (2011)ADSCrossRefGoogle Scholar
  24. 24.
    A.S. Alofi, Int. Math. Forum 7, 2639 (2012)MathSciNetGoogle Scholar
  25. 25.
    H. Zhang, Commun. Nonlinear Sci. Numer. Simul. 12, 627 (2007)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    N.Z. Petrovic, M. Bohra, Opt. Quantum Electron. 48, 268 (2016)CrossRefGoogle Scholar
  27. 27.
    Z. Yan, J. Phys. A 36, 1961 (2003)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    M.A. Akbar, N.H.M. Ali, Prog. Appl. Math. 1, 30 (2011)Google Scholar
  29. 29.
    J.H. He, X.H. Wu, Chaos, Soliton Fractals 30, 700 (2006)ADSCrossRefGoogle Scholar
  30. 30.
    N. Kadkhoda, H. Jafari, Optik 139, 72 (2017)ADSCrossRefGoogle Scholar
  31. 31.
    F. Ozpinar, H.M. Baskonus, H. Bulut, Entropy 17, 8267 (2015)ADSCrossRefGoogle Scholar
  32. 32.
    L. Zhang, K. Sun, S. He, H. Wang, Y. Xu, Eur. Phys. J. Plus 132, 31 (2017)ADSCrossRefGoogle Scholar
  33. 33.
    X.J. Yang, F. Gao, H.M. Srivastava, Comput. Math. Appl. 73, 203 (2017)MathSciNetCrossRefGoogle Scholar
  34. 34.
    A. Atangana, J.F. Botha, J. Earth Sci. Clim. Change 3, 115 (2012)CrossRefGoogle Scholar
  35. 35.
    A. Atangana, B.S.T. Alkahtani, Arab. J. Geosci. 9, 8 (2017)CrossRefGoogle Scholar
  36. 36.
    A.M. Wazwaz, J. Math. Phys. 16, 1212 (1977)Google Scholar
  37. 37.
    K.A. Touchent, F.M. Belgacem, Nonlinear Stud. 22, 591 (2015)MathSciNetGoogle Scholar
  38. 38.
    M.G. Hafez, M.N. Alam, M.A. Akbar, King Saud Univ. J. Sci. 27, 105 (2015)CrossRefGoogle Scholar
  39. 39.
    H. Naher, F.A. Abdullah, M.A. Akbar, PLoS ONE 8, e64618 (2013)ADSCrossRefGoogle Scholar
  40. 40.
    C. Yan, Phys. Lett. A 22, 77 (1996)ADSCrossRefGoogle Scholar
  41. 41.
    H.M. Baskonus, Nonlinear Dyn. 86, 177 (2016)MathSciNetCrossRefGoogle Scholar
  42. 42.
    H.M. Baskonus, H. Bulut, T.A. Sulaiman, Indian J. Phys. 135, 327 (2017)Google Scholar
  43. 43.
    H. Bulut, T.A. Sulaiman, H.M. Baskonus, F. Erdogan, Eur. Phys. J. Plus 132, 350 (2017)CrossRefGoogle Scholar
  44. 44.
    Y. Sun, B. Tian, H.L. Zhen, X.Y. Wu, X.Y. Xie, Mod. Phys. Lett. B 30, 16502134 (2016)Google Scholar
  45. 45.
    E.M.E. Zayed, J. Phys. A: Math. Theor. 42, 195202 (2009)ADSCrossRefGoogle Scholar
  46. 46.
    H. Naher, F.A. Abdullah, M.A. Akbar, J. Appl. Math. 2012, 575387 (2012)Google Scholar
  47. 47.
    E.W. Weisstein, Concise Encyclopedia of Mathematics, 2nd edition (CRC Press, New York, 2002)Google Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of EducationErciyes UniversityKayseriTurkey
  2. 2.Department of MathematicsFirat UniversityElazigTurkey
  3. 3.Department of Computer EngineeringMunzur UniversityTunceliTurkey

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